It is known that artificial intelligence (AI) and fuzzy logic are strongly related. Actually, the role of AI is to make a computer simulate a human being in handling both certainty and uncertainty informations; and a basic tool for computers in dealing with those kind of informations is logic. Classical logic deals with certain informations whereas many-valued logic (fuzzy logic) known as nonclassical logic, deals with uncertain and fuzzy informations. Nowadays, nonclassical logic has become a very useful technique for computer science to deal with such (uncertain and fuzzy) informations. One of the most famous nonclassical logic is the MTL-logic which has been introduced in 2001 by Godo and Esteva [1]}. But three years before, in 1998, Hájek introduced a very general many-valued logic, called Basic Logic [2]}. Since a t-norm has a residuum if and only if the t-norm is left continuous, then the Basic Logic is not the most general t-norm-based logic. Indeed the MTL-logic was proved by Jenei and Montagna [3]} to be the most general t-norm based logic with residua.
